Standard thermal ink jet printheads, operated in a conventional manner, eject an essentially fixed ink mass from each nozzle.
Drop mass modulation, the process where ejected ink mass is varied on demand, can substantially enhance the quality of printed output. Ink jet and other non-impact printers have long been contemplated as particularly well suited to the production of continuous and half tone images because of the ability to produce a spot at any location on a sheet of paper. However, the ability of ink jet printers to produce continuous and half tone images has been quite limited due to the fact that most ink jet printheads can only produce droplets having fixed volume. As a result, ink spots produced by such droplets are of a fixed size. Furthermore, ink jet printheads typically use a fixed resolution, typically 300-400 dots per inch or lower, to place droplets on a sheet of paper. This is not sufficient to produce half-tone images which require higher print quality.
The quality of printed output can also be enhanced by increased print resolution where the number of droplets per square inch is increased, for example, from 300.times.300 dots per inch matrix to 600.times.600 dots per inch matrix. Drop mass modulation is often preferred over increased print resolution. This is because drop size modulation does not significantly increase print head complexity and because it requires a smaller increase in data handling capability than does a comparable increase in print resolution. This difference in data handling capability is often unappreciated and, therefore, a brief theoretical discussion is provided below highlighting the theoretical advantages of drop size modulation over increased print resolution.
In their simplest form, digital print mechanisms operate by filling a pattern of dot positions on a square grid on the printed page. Information is represented by devoting a single byte to each dot position in an R.times.R grid. The symbol R denotes print resolution, which is traditionally described by the number of dots per inch on one side of the grid. Each byte is comprised of an integral number of bits. Each bit b conveys one of two possible states; hence the term binary state: EQU b=0 or 1.
Each byte B.sub.k is comprised of k bits, where k can be any positive integer: EQU B.sub.k =(b.sub.1, b.sub.2, . . . , b.sub.k).
A byte B.sub.k has two relevant properties: the number N.sub.k of bits of which it is comprised: EQU N.sub.k =N(B.sub.k)=k,
and the number S.sub.k of possible states conveyed: EQU S.sub.k =S(B.sub.k)=2.sup.k.
Hence, a byte B.sub.1 contains a single bit and conveys two states; a byte B.sub.2 contains two bits and conveys four states; and a byte B.sub.3 contains three bits and conveys eight states, and so forth for larger values of k where: EQU B.sub.1 =(0) or (1), EQU B.sub.2 =(0,0) or (0,1) or (1,0) or (1,1), EQU B.sub.3 =(0,0,0) or (0,0,1) or (0,1,0) or (0,1,1) or (1,0,0) or (1,0,1) or (1,1,0) or (1,1,1).
Standard monochrome printing (with no dot size modulation) requires one B.sub.1 -sized byte for every dot in the print grid. Hence, a volume V.sub.0 of data is required to print a unit grid, where: EQU V.sub.0 =N.sub.1 .times.R.sup.2 =R.sup.2
If print resolution R is increased by a factor F, then the required data volume per unit print grid becomes EQU V.sub.1 =N.sub.1 .times.(FR).sup.2,=F.sup.2 R.sup.2,=F.sup.2 V.sub.0
Hence, the data volume increases by a multiplicative factor F.sup.2 when print resolution increases by a factor F.
Suppose that, as an alternative to increasing print resolution, the number of printable dot states M increases from two (dot or void) to some larger integer number. The additional information is represented by increasing the size of the byte associated with each position of the print grid. The smallest byte that conveys M dot states is one with k bits, where k is the smallest positive integer that satisfies the inequality EQU M.ltoreq.S.sub.k =2.sup.k.
Hence, while the possible states of a simple dot with no size modulation can be conveyed with a byte B.sub.1 (with two states), the state of a dot with two or three possible sizes can be conveyed with a byte B.sub.2 (with four states). The data volume requirement for dot size modulation can be compared to that of standard monochrome printing. The data volume V.sub.2 per unit grid, required to print dots with M possible states, is given by EQU V.sub.2 =N.sub.k .times.R.sup.2,=kR.sup.2 ,=kV.sub.0,
where k is the smallest positive integer that satisfies the above inequality.
Hence, data volume increases by a multiplicative factor k as the number of dot states increases from two to M at fixed print resolution. It is instructive to express the data volume V.sub.2 directly in terms of the parameter M. Recall that the number of bits k is the smallest positive integer that satisfies the inequality M.ltoreq.2.sup.k. If we take the natural logarithm of both sides of the inequality, we obtain EQU log M.ltoreq.k log 2.
Therefore, we can make a substitution in the formula for V.sub.2 : EQU V.sub.2 =kV.sub.0 .gtoreq.(log M/log 2)V.sub.0
Hence, it can be said that the data volume V.sub.2, characterizing the addition of dot states M, increases roughly as the natural logarithm of M. Thus, in terms of increasing print quality, dot size modulation is preferred to increasing print resolution, since the logarithm function grows dramatically slower than the square function that characterizes the relationship between data volume and print resolution.
Even considering the major theoretical advantages of drop size modulation, no workable system has yet been developed, although various strategies have been attempted to modulate the size of an ink drop being ejected. Many patents have focused on adjusting the amplitude of the voltage pulse and/or the timing of each of the voltage pulses. See, for example, Tsuzuki et al. U.S. Pat. No. 4,281,333; Lee et al. U.S. Pat. No. 4,513,299; DeBonte et al. U.S. Pat. No. 5,202,659. These patents suffer from the disadvantage that each requires a complex control circuit and large data handling capability.
Chip temperature control schemes have also been attempted with limited success, see Wysocki et al. U.S. Pat. No. 5,223,853. Other methods focus on fluid dynamics of the meniscus of the ejected droplet, see Burr et al. U.S. Pat. No. 5,495,270.
A different approach, using simplified control circuits is disclosed in U.S. Pat. No. 4,499,479. The '479 patent discloses an ink jet drop-on-demand printing system comprising a transducer having a plurality of separately actuable sections. This patent is directed to a side-shooter type printhead. Print data is provided which defines a selected drop volume and control means is provided which is operable in response to print data to produce signals to selectively actuate a particular combination of the separately actuable sections of the transducer to produce a drop of a volume specified by the print data. To provide further control over the drop volume, in a second embodiment, while maintaining the drop of velocity within selected limits, the amplitude of the drive signals can also be varied. In a first embodiment, the piezoelectric transducer sections are of an equal length, whereas in the second embodiment the transducer sections are of unequal length. Disadvantageously, this patented design requires a relatively complicated structure for exciting the ink in ink cavity. Furthermore, it is difficult to predict the variation of drop volume with amplitude and pulse width at constant drop velocity as described in that patent. The '479 patent recognized that generating a drop size look-up table would be difficult because of the large number of interrelated factors which affect the printhead operation. The large number of factors include the different distances that each of the separately actuable sections are disposed from the nozzle as well as the interrelationship between each of the separately actuable sections. See U.S. Pat. No. 4,730,197 which describes and characterizes numerous interactions between ink jet geometric features, drive waveforms, meniscus resonance, pressure chamber resonance, and ink jet ejection characteristics.
Accordingly, a need still exists in the art for a printhead capable of drop size modulation having simplified geometric features, using simplified control circuits and which reduces the data handling requirement of the digital print controller.